Tagged Questions
3
votes
1answer
172 views
How to calculate the area between 2 polar curves: $r=\frac{4}{2}-\sin\theta$ and $r=3\sin\theta$?
How to calculate the area between 2 polar curves: $r=2-\sin\theta$ and $r=3\sin\theta$?
I know that one curve is a limaçon and the other is a circle. I have them drawn out as well, my only question ...
3
votes
1answer
386 views
Bézier approximation of archimedes spiral?
As part of an iOS app I’m making, I want to draw a decent approximation of an Archimedes spiral. The drawing library I’m using (CGPath in Quartz 2D, which is C-based) supports arcs as well as cubic ...
1
vote
2answers
129 views
Length of a plane curve in polar coordinate
Consider the plane curve $\gamma$ in polar coordinates:
$$
r=r_0+e^{\lambda\theta}, \quad \theta_1 \le \theta \le \theta_2,
$$
where $r_0,\lambda,\theta_1>0$. Is it possible to compute explicitly ...
1
vote
1answer
197 views
Find the area of the region determined by two curves
Find the area of the region $R$ given by two curves.
So the region $R$ describes the area that is common between the two curves:
$$\begin{align*}
\text{Function 1: } r&= 2\sin(\theta)\\
...
5
votes
2answers
663 views
Is $r=2\cos(\theta)$ a one-petal polar function?
I'm currently learning about polar functions and their graphs in precalculus, and one of the questions on my homework is to identify the shape of the function $r=2\cos(\theta)$. We were taught that ...
1
vote
2answers
2k views
Difficult conversion from polar equation to rectangular equation.
How do we convert this into rectangular equation?
$r=5\theta$
0
votes
2answers
125 views
How do we get the rectangular form of this?
I know if $\sqrt{x^2+y^2} = x$, then the polar equation of this is $r=cos\theta$
So,how to get the rectangular form of this polar equation, is it complicate:
$r=cos(10\theta)$
3
votes
3answers
1k views
Writing a Polar Equation for the Graph of an Implicit Cartesian Equation
If $(x^2+y^2)^3=4x^2y^2,$ then $r=\sin 2\theta$ for some $\theta$.
Using $r^2=x^2+y^2, x=r\cos\theta,y=r\sin\theta$, it's easy to get $r^2=\sin^22\theta$.
But I don't know what to do next, since ...
0
votes
1answer
272 views
definition of sinusoidal curve
I have question related with these two definition:
In geometry, the sinusoidal spirals are a family of curves defined by the equation in polar coordinates
$$r^n = a^n \cos(n \theta)$$
where $a$ is ...
2
votes
2answers
2k views
Polar to Parametric Equation?
I'm struggling with this problem, I'm still only on part (a). I tried X=rcos(theta) Y=rsin(theta) but I don't think I'm doing it right.
Curve C has polar equation ...
1
vote
2answers
393 views
Express this curve in the rectangular form
Express the curve $r = 9/(4+\sin \theta)$ in rectangular form.
And what is the rectangular form?
if I get the expression in rectangular form, how am I able to convert it back to polar ...
5
votes
6answers
742 views
Why, conceptually, do limaçons $r=a+b\cos\theta$ have dimples when $|\frac{a}{b}|<2$?
Using calculus, I can justify that limaçons—the polar graphs of $r=a+b\cos\theta$ for various nonzero real values of $a$ and $b$—are dimpled when $|\frac{a}{b}|<2$, but that doesn't seem to yield ...
6
votes
2answers
239 views
Need help with Curves and parameterizations
I'm having some trouble solving a couple of problems:
I know this one must be pretty easy but can't find the way to solve it.
I need to find the arc length of a curve described by $ r=1- ...
